Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration

Mensuration Exercise 20A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
The length and the breadth of a rectangular plot are 135 m and 65 m. Find, its perimeter and the cost of fencing it at the rate of ₹60 per m.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 1

Question 2.
The length and breadth of a rectangular field are in the ratio 7 : 4. If its perimeter is 440 m, find its length and breadth. Also, find the cost of fencing it @ ₹150 per m.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 2

Question 3.
The length of a rectangular field is 30 m and its diagonal is 34 m. Find the breadth of the field and its perimeter.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 3

Question 4.
The diagonal of a square is 12\(\sqrt { 2 } \) cm. Find its perimeter.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 4

Question 5.
Find the perimeter of a rectangle whose length = 22.5 m and breadth = 16 dm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 5

Question 6.
Find the perimeter of a rectangle with length = 24 cm and diagonal = 25 cm
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 6

Question 7.
The length and breadth of rectangular piece of land are in the ratio of 5 : 3. If the total cost of fencing it at the rate of ₹48 per metre is ₹19,200, find its length and breadth.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 7

Question 8.
A wire is in the shape of square of side 20 cm. If the wire is bent into a rectangle of length 24 cm, find its breadth.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 8

Question 9.
If P = perimeter of a rectangle, l= its length and b = its breadth find :
(i) P, if l = 38 cm and b = 27 cm
(ii) b, if P = 88 cm and l = 24 cm
(iii) l, if P = 96 m and b = 28 m
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 9
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 10

Question 10.
The cost of fencing a square field at the rate of
Cost of fencing 440 m = ₹150 x 440 = ₹75 per meter is
Cost of fencing 440 m = ₹150 x 440 = ₹67,500. Find the perimeter and the side of the square field.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 11

Question 11.
The length and the breadth of a rectangle are 36 cm and 28 cm. If its perimeter is equal to the perimeter of a square, find the side of the square.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 12

Question 12.
The radius of a circle is 21 cm. Find the circumference (Take π = 3 \(\frac { 1 }{ 7 }\) ).
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 13

Question 13.
The circumference of a circle is 440 cm. Find its radius and diameter. (Take π = \(\frac { 22 }{ 7 }\)
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 14

Question 14.
The diameter of a circular field is 56 m. Find its circumference and cost of fencing it at the rate of ₹80 per m. (Take n = \(\frac { 22 }{ 7 }\))
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 15

Question 15.
The radii of two circles are 20 cm and 13 cm. Find the difference between their circumferences. (Take π = \(\frac { 22 }{ 7 }\))
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 16

Question 16.
The diameter of a circle is 42 cm, find its perimeter. If the perimeter of the circle is doubled, what will be the radius of the new circle. (Take π = \(\frac { 22 }{ 7 }\) )
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 17

Question 17.
The perimeter of a square and the circumference of a circle are equal. If the length of each side of the square is 22 cm, find:
(i) perimeter of the square.
(ii) circumference of the circle.
(iii) radius of the circle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 18

Question 18.
Find the radius of the circle whose circumference is equal to the sum of the circumferences of the circles having radii 15 cm and 8 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 19

Question 19.
Find the diameter of a circle whose circumference is equal to the sum of circumference of circles with radii 10 cm, 12 cm and 18 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 20

Question 20.
The circumference of a circle is eigth time the circumference of the circle with radius 12 cm. Find its diameter.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 21

Question 21.
The radii of two circles are in the ratio 3 : 5, find the ratio between their circumferences.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 22

Question 22.
The circumferences of two circles are in the ratio 5 : 7, find the ratio between their radii.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 23

Question 23.
The perimeters of two squares are in the ratio 8:15, find the ratio between the lengths of their sides.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 24

Question 24.
The lengths of the sides of two squares are in the ratio 8:15, find the ratio between their perimeters.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 25

Question 25.
Each side of a square is 44 cm. Find its perimeter. If this perimeter is equal to the circumference of a circle, find the radius of the circle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20A 26

Mensuration Exercise 20B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Find the area of a rectangle whose length and breadth are 25 cm and 16 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 27

Question 2.
The diagonal of a rectangular board is 1 m and its length is 96 cm. Find the area of the board.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 28

Question 3.
The sides of a rectangular park are in the ratio 4 : 3. If its area is 1728 m2, find
(i) its perimeter
(ii) cost of fencing it at the rate of ₹40 per meter.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 29

Question 4.
A floor is 40 m long and 15 m broad. It is covered with tiles, each measuring 60 cm by 50 cm. Find the number of tiles required to cover the floor.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 30

Question 5.
The length and breadth of a rectangular piece of land are in the ratio 5 : 3. If the total cost of fencing it at the rate of ₹24 per meter is ₹9600, find its :
(i) length and breadth
(ii) area
(iii) cost of levelling at the rate of ₹60 per m2.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 31

Question 6.
Find the area of the square whose perimeter is 56 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 32

Question 7.
A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m2 find the area of the lawn.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 33

Question 8.
For each figure, given below, find the area of shaded region : (All measurements are in cm)
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B Q8
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 34
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 35

Question 9.
One side of a parallelogram is 20 cm and its distance from the opposite side is 16 cm. Find the area of the parallelogram.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 36

Question 10.
The base of a parallelogram is thrice it height. If its area is 768 cm2, find the base and the height of the parallelogram.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 37

Question 11.
Find the area of the rhombus, if its diagonals are 30 cm and 24 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 38

Question 12.
If the area of a rhombus is 112 cm2 and one of its diagonals is 14 cm, find its other diagonal.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 39

Question 13.
One side of a parallelogram is 18 cm and its area is 153 cm2. Find the distance of the given side from its opposite side.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 40

Question 14.
The adjacent sides of a parallelogram are 15 cm and 10 cm. If the distance between the longer sides is 6 cm, find the distance between the shorter sides.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 41

Question 15.
The area of a rhombus is 84 cm2 and its perimeter is 56 cm. Find its height.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 42

Question 16.
Find the area of a triangle whose base is 30 cm and height is 18 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 43

Question 17.
Find the height of a triangle whose base is 18 cm and area is 270 cm2.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 44

Question 18.
The area of a right-angled triangle is 160 cm2. If its one leg is 16 cm long, find the length of the other leg.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 45

Question 19.
Find the area of a right-angled triangle whose hypotenuse is 13 cm long and one of its legs is 12 cm long.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 46
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 47

Question 20.
Find the area of an equilateral triangle whose each side is 16 cm. (Take \(\sqrt { 3 } \)= 1.73)
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 48

Question 21.
The sides of a triangle are 21 cm, 17 cm and 10 cm. Find its area.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 49

Question 22.
Find the area of an isosceles triangle whose base is 16 cm and length of each of the equal sides is 10 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 50
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 51

Question 23.
Find the base of a triangle whose area is 360 cm2and height is 24 cm.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 52

Question 24.
The legs of a right-angled triangle are in the ratio 4 :3 and its area is 4056 cm2. Find the length of its legs.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 53
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 54

Question 25.
The area of an equilateral triangle is (64 x \(\sqrt { 3 } \) ) cm2– Find the length of each side of the triangle.
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 55

Question 26.
The sides of a triangle are in the ratio 15 : 13 : 14 and its perimeter is 168 cm. Find the area of the triangle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 56

Question 27.
The diameter of a circle is 20 cm. Taking π = 3.14, find the circumference and its area.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 57

Question 28.
The circumference of a circle exceeds its diameter by 18 cm. Find the radius of the circle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 58

Question 29.
The ratio between the radii of two circles is 5 : 7. Find the ratio between their :
(i) circumference
(ii) areas
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 59
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 60

Question 30.
The ratio between the areas of two circles is 16 : 9. Find the ratio between their :
(i) radii
(ii) diameters
(iii) circumference
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 61
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 62

Question 31.
A circular racing track has inner circumference 528 m and outer circumference 616 m. Find the width of the track.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 63

Question 32.
The inner circumference of a circular track is 264 m and the width of the track is 7 m. Find:
(i) the radius of the inner track.
(ii) the radius of the outer circumference.
(iii) the length of the outer circumference.
(iv) the cost of fencing the outer circumference at the rate of ₹50 per m.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 64

Question 33.
The diameter of every wheel of a car is 63 cm. How much distance will the car move during 2000 revolutions of its wheel.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 65

Question 34.
The diameter of the wheel of a car is 70 cm. How many revolutions will it make to travel one kilometre?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 66

Question 35.
A metal wire, when bent in the form of a square of largest area, encloses an area of 484 cm2. Find the length of the wire. If the same wire is bent to a largest circle, find:
(i) radius of the circle formed.
(ii) area of the circle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 67

Question 36.
A wire is along the boundary of a circle with radius 28 cm. If the same wire is bent in the form of a square, find the area of the square formed.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 68

Question 37.
The length and the breadth of a rectangular paper are 35 cm and 22 cm. Find the area of the largest circle which can be cut out of this paper.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 69

Question 38.
From each comer of a rectangular paper (30 cm x 20 cm) a quadrant of a circle of radius 7 cm is cut. Find the area of the remaining paper i.e., shaded portion.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B Q38
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 20 Mensuration Ex 20B 70

Selina Concise Mathematics Class 7 ICSE Solutions